Since they are tied to our hard-copy newsletter and monthly
meetings, look for Puzzle Updates, usually on the Friday before the Second
Wednesday of each Month!

Next Puzzle Posting: October 6th, 2017

SEPTEMBER 2017 PUZZLE - "How High the Sun?"

Submitted by Dave Thomas

The diagram below indicates a method whereby one could use measurements of the sun's elevation
on the vernal or autumnal equinox to calculate the height of the sun above the earth in Voliva's flat earth model. In this
diagram, an observer at 45o latitude would see the sun at that same angle above the horizon, and will be 1/8th of the
24,000-mile diameter of the flat earth away from the equator, i.e. 3,000 miles. The "height" of the sun would be calculated
as 3,000 miles for this latitude.

The September Bonus:What would the following people, using the method above, calculate for the height of the sun
above the flat earth, as seen on the autumnal equinox?

A commuter using a bicycle has a two-mile ride to work. Going to the office, the path is level for a
half mile, then runs uphill at a 10% grade for one mile, then downhill at a 10% grade for a quarter mile, and finally uphill for a
quarter mile at a 20% grade. The commuter goes ten mph on a level surface, half that for a 10% uphill grade, three-halves that for
a 10% downhill grade, and one-quarter that for a 20% uphill grade. For a 20% downhill grade, the rider purposely limits his speed
to no more than that for the 10% downhill grade.

According to the Standard Model of physics, a proton is composed of 3 quarks (two ups and one down),
with a positive charge of 2/3 + 2/3 - 1/3 = 3/3 = 1. While a neutron is likewise made of 3 quarks (one
up and two downs), it has a neutral charge of 2/3 - 1/3 – 1/3 = 0/3 = 0.

The May Bonus:
The combined masses of the three quarks of a proton or neutron constitute what percentage of the rest mass of that proton or neutron?

1%

50%

97%

110%

Hall of Fame (May Puzzle Solvers):

Rocky S. Stone (NM)

Submitted by Dave Thomas

Consider the Pythagorean Scale, for which the frequency ratios to the lower C note are shown above.
In the Well-Tempered Scale, on the other hand, the ratio of each note to the one preceding it is a
constant 21/12.

The April Bonus:
For the C-scale starting at 256 Hz, what note has the largest difference between well-tempered and Pythagorean scales? How many hertz off is it?

A few weeks after the inauguaration of President John F. Kennedy, a math teacher at a small southwestern
college told his students that they were living in a very special year. The professor said "The last time
this happened, Billy the Kid was being tracked by Pat Garrett. The time before that, Suleiman II ended his
reign as sultan of the Ottoman Empire."

The March Bonus:
When was (or is) the next time this type of “Special Year” occurred (or will occur)?

Jim wants to make a political sign. At the art store, letters are priced according to a simple logical rule.
Jim finds that he can purchase the letters to spell TRUMP for $11, PENCE for $12, and BANNON for $14.

The February Bonus:
How much will Jim need to buy the letters for IMPEACH?

The December Bonus:
For the 2016 US Presidential Election, what is the maximum difference in the Popular Vote that could still
result in a losing Electoral Vote?
Use these data (an Excel spreadsheet with these data is available at www.nmsr.org/electoral.xls).

Fred's turkey farm has a total of 100 Toms and Hens, having a net weight of 1,650 pounds. The distribution of turkey weights is remarkably uniform for each gender, and the typical Tom weighs twice as much as a typical Hen.

The November Bonus: (A) What is the largest possible Hen’s weight? How many Toms and Hens are there for this weight?
(B) What is the largest Hen’s weight that is a round number of pounds? How many Toms and Hens?
(C) With an equal number of Toms and Hens, what is a typical Hen’s weight? How many Toms (= # Hens)?
(D) What is the smallest Hen’s weight that is a round number of pounds? How many Toms and Hens? And
(E) What is the smallest possible Hen’s weight? How many Toms and Hens?

You have a cannon, which can be controlled by its tilt angle and by the muzzle velocity v0. Assume that the muzzle
velocity v0 is kept constant, and that the tilt angle can be varied, from shooting straight up, to shooting horizontally,
as shown in the figure above.

The May Bonus:The thicker line in the figure above shows the envelope of all the positions the cannon can
reach at constant muzzle velocity. What is the equation of this envelope?

Hall of Fame (May Puzzle Solvers):

Eric Hanczyc (WA)
Brian Pasko (NM)

APRIL 2016 PUZZLE - "Really Rolling Now!"

Submitted by Dave Thomas

Given the moment of inertia for a toilet paper roll from last month, suppose that two identical rolls are dropped at
the same time. The first roll is dropped from a height h1, and allowed to free-fall to the floor. The second
roll is held onto by someone's hand at a height h2, and unrolls as it falls.

The April Bonus:Assuming that the drop height is small enough that the roll's moment of inertia remains
constant during the fall, what is the ratio of h2 to h1 to make the rolls land at the same instant?

The March Bonus:(A) What is the sheet thickness, ΔT? (B) What is the moment of inertia of the roll, both initially, and as a function of radius r?

Hall of Fame (March Puzzle Solvers):

Eric Hanczyc (WA)
Keith Gilbert (NM)
Brian Pasko (NM)

FEBRUARY 2016 PUZZLE - "Gardening Time"

Submitted by Dave Thomas

You are busy in the garden, whipping up a batch of fertilizer for the plants. You need to measure exactly five
gallons of water for the mix, but all you have at hand are two buckets (one has a three-gallon capacity, while the
other holds seven-gallons). Neither bucket is graduated with gallon marks. You can get as much water as you you
need from the hose, and any excess water can be used in the garden.
Being clever, you quickly realize a method for using the two buckets to get exactly five gallons of water.

The February Bonus:How many gallons of water need to be supplied from the hose? And how many excess gallons of water will you pour into the garden?

The Three Stooges went to a cafe, and ordered a pizza for $15. They each contributed $5. The waiter took the money to the chef, who was a friend of the Stooges, and asked the waiter to return $5 to them.

The waiter was lazy and dishonest, however, and instead of splitting the $5 fairly between the three, he just gave them $1 each, and pocketed the remaining $2 for himself.

Now, Moe, Larry and Curly each had effectively paid $4, so the sum actually shelled out was $12. Along with the $2 in the waiter's pocket, everything totalled $14.

Two types of intelligent bipedal organisms live on planet Blarnia: obligate liars and obligate truth tellers. The ambassador from Earth met with three Blarnians to negotiate a peace pact. One Blarnian spoke, but the ambassador didn't catch it. The second one remarked, "He said he was a liar." The third Blarnian yelled at the second, "You are lying!"

You're a naturalist trying to make sense out of cicada breeding patterns. The cicadas appear in different broods, and it appears that it's best for each brood if fewer other broods come out in their preferred breeding years. That minimizes the chances of genetic mixing between broods, and helps maintain brood lines.

The October Bonus:

If red cicadas brood every 7 years, and green cicadas every 14 years, how many years will it be between years where both broods make their appearance?

If red cicadas brood every 7 years, and green cicadas every 13 years, how many years will it be between years where both broods make their appearance?

You're in a spaceship traveling at half of lightspeed relative to the Milky Way, and you need to reduce your speed to zero in order to disembark and visit Aunt Edna.

The August Bonus:

Assuming that you can withstand the strain of 10 gees for some time, how long will it take to decelerate? (Assume one gee is 10 meters per second squared.)

After deciding against torturing yourself for such a long time, you decide to take it a little easier, seven times easier to be precise. With a deceleration of 1.428 gees for some time, how long will it take to stop?

Assuming that you can withstand the strain of 10 gees for 10 seconds, and that you'll need a full hour to recuperate from each grueling 10-second ordeal, what is your reduction in speed for one such event? And how many such efforts will it take to decelerate to zero meters/second?

A driver on the interstate notices that, between every pair of adjacent mile markers, he encounters 30 cars in the oncoming lanes, on average.

The August Bonus:

Assuming that cars in both directions are going the legal limit, what is the actual density of cars per mile for the oncoming lanes?

A radio report informs the driver that that cars in the oncoming direction are going half of the legal limit, while cars going in his direction are doing the limit. What is the actual density of cars per mile for the oncoming lanes?

A radio report informs the driver that that cars in the oncoming direction are going the legal limit, while cars going in his direction are doing half of the limit. What is the actual density of cars per mile for the oncoming lanes?

A train departs from New York City (NYC), heading toward Los Angeles (LA) at 100 mph. 3.5 hours later, a train departs from LA heading toward NYC at 200 mph. Assume there are 2000 miles of track between LA and NYC.

The July Bonus:(A) When do they meet?
(B) When they meet, which train is closer to NYC?

Assume a particular radioactive isotope (say, Uranium 238) has a "slow" half-life of TS (say, 4.48 billion years). Suppose that a sample has been collected from a given rock, and that the ratio of daughter isotope of lead (Pb206) to parent isotope (U238) in the sample is RS = 0.295. Likewise, a sample of a different radio-isotope (say, Uranium 235) with a "fast" half-life of TF (say, 704 million years) has also been collected from the same rock, and its ratio of daughter isotope (Pb207) to parent isotope (U235) is RF = 9.09.

Concordia/Discordia Chart: the horizontal axis is the fast daughter/parent ratio RF, and the vertical axis is the slow daughter/parent ratio RS.

The June Bonus:(A) In terms of the given halflife TH and current daughter/parent ratio R, what is the simplest, most elegant formula for predicting what the new value of the ratio will be after an additional passage of time of ΔT years? (Hint: the formula will have one positive exponent, no reciprocals, and just one pair of parentheses.)

(B) What will the ratios (RF, RS) = (9.09, 0.295) become after an additional time interval ΔT of 1 billion years?

(C) What will the ratios (RF, RS) = (18.18, 0.590) become after an additional time interval ΔT of 1 billion years?

Hall of Fame (June Puzzle Solvers):

Eric Hanczyc (WA)
Alice Anderson(NM)
Brian Pasko (NM)

May 2015 PUZZLE - "To Infinity, and Beyond!"

Submitted by Dave Thomas

For this puzzle, assume X is any non-zero number, and consider the iterative process in which X is replaced by 2 + 15/X.

Farmer Jones owns four times as many sheep as cattle. The grass on his farm is currently 12 inches high, and grows at a rate of two inches per day.

The grass on one acre of Farmer Jones' farm can support a dozen cattle for six days, accounting for daily growth. Alternatively, one acre of Farmer Jones' farm grass can support three dozen sheep for twelve days, again accounting for growth.

The April Bonus:What is the number of cattle and sheep per acre that will allow the land to support the livestock indefinitely? (Or at least, for the entire growing season?)

To win the Powerball jackpot one must choose five different numbers from 1 to 59, plus the Powerball number from one of 35 numbers. The bet is two dollars. One can win in nine ways: the largest prize is for matching all 5 numbers and the Powerball, and is a variable amount. The other 8 amounts are fixed payouts. Here are all nine ways to win, and their prize amounts:

5 numbers + Powerball (PB): JACKPOT

5 numbers:$1,000,000

4 numbers +PB:$10,000

4 numbers:$100

3 numbers +PB:$100

3 numbers:$7

2 numbers +PB:$7

1 number +PB:$4

PB only: 4$

The February Bonus:What is the jackpot amount for an even bet (expected winnings = zero), for the situation in which (A) only the jackpot is considered, and the situation in which (B) all nine prizes are considered?

Hall of Fame (February Puzzle Solvers):

Eric Hanczyc (WA)
Brian Pasko* (NM)
Alice Anderson* (NM)
* Part (A)

January 2015 PUZZLE - "Moving Sidewalk"

Submitted by Dave Thomas

When his parent's holiday flight was cancelled because of snow, bored little Bobby decided
to do some physics experiments on the Moving Sidewalk. He found that it took three minutes to go the length of the
Sidewalk if he walked at his normal speed in the same direction as the Sidewalk was moving. He also found it took
him six minutes to go the same length walking normally in the "wrong" direction.

The January Bonus:When the snow caused a blackout, the Moving Sidewalk stopped working. How many minutes did it take Bobby to walk
the full length of the disabled Sidewalk?

A frugal bachelor has exactly seven pairs of socks; four pairs are black, and three are white.

The December Bonus:If all 14 socks are lying around in random positions inside the bachelor's dryer, and he grabs the first two socks he can find in the dark, what is the probability he'll have (A) A black pair? (B) A white pair? (C) No pair at all?

A certain stalker was tailing the target of his desires at the mall. As his prey entered several stores in the mall, the stalker would also enter the same store, but would always buy something to allay suspicion.

At the first store his victim entered, the stalker spent a third of the money he had on his person. At the second store, he spent a third of the remaining amount. And at the third store, he again spent a third of the remaining amount.

The November Bonus:If the stalker spent $38 all together, how much did he start with?

James Randi, Michael Shermer, Richard Dawkins, and Neil deGrasse Tyson were all entered in a charity volleyball game. The sponsors printed up special jerseys with each of the four men's names. When Randi mischievously suggested that everyone wear another's jersey, all agreed with his marvelous prank.

The October Bonus:From the following information, deduce who was wearing each jersey:

A hinged rod of length L is held at rest at an angle θ, and then released. At precisely the same moment, a steel ball is released from the same height as the top of the rod.

The September Bonus:If vrod is the speed of the tip of the rod as it hits the flat table top, and vff is the speed of the free-falling steel ball as it impacts the same table top, what is the ratio of vrod to vff ?

Hall of Fame (September Puzzle Solvers):

Keith Gilbert (NM)
Eric Hanczyc (WA)
Eiichi Fukushima (NM)

August 2014 PUZZLE - "The Physicist's Spouse"

Submitted by Dave Thomas

A physicist's spouse used a wheelchair, and this was firmly hooked to latches on the van's
floor during excursions. The physicist wanted to minimize accelerations and decelerations while driving, as these were
uncomfortable for his passenger. As they were cruising along at 12 meters/second (~27 mph), a red light turned on at
the stop bar of the next intersection, a mere six meters away.

The August Bonus:Assuming the physicist applied constant brake pressure during the stop, and reduced the
van's speed to zero just as it reached the stop bar, what was the time τ for the braking maneuver? And what was the
constant acceleration ao required?

BONUS Bonus #2: Suppose the physicist used a linear deceleration rate, such that he covered the six meters in a time τ , starting at zero acceleration, and ending with zero speed, and acceleration ao at the stop bar. What is the time τ for this braking maneuver, and what is the final acceleration ao?

BONUS Bonus #3: Suppose the physicist used a linear deceleration rate, such that he covered the six meters in a time τ , starting at acceleration ao, and ending with zero speed and zero acceleration at the stop bar. What is the time τ for this braking maneuver, and what is the initial acceleration ao?

BONUS Bonus #4: In all three bonuses, the area under the acceleration curve from 0 to τ is the same for the two givens (6 meters to stop from an initial speed of 12 m/s). What is this area, and what does it signify? And, which of the three alternatives given is the best for the delicate spouse?

Hall of Fame (August Puzzle Solvers):

Keith Gilbert (NM)
Eric Hanczyc (WA)

July 2014 PUZZLE - "Gettin' Both Trucks Home"

Based on a True Story

University of Texas at Austin biologist David Hillis has a favorite "stuck in the middle
of nowhere" story with a happy ending. He was out in his truck, hours away from Austin, when his alternator light came
on. He watched his voltmeter drop until the truck stopped, hundreds of miles away from the closest place that could
repair the alternator. Luckily for Hillis, his good friend Jim happened to drive by, and stopped to help. David Hillis
could have ridden back to Austin with Jim, of course, but then his truck with its broken alternator and drained battery
would still have been stuck in the middle of nowhere. Using one truck to tow the other was not feasible, either. However,
the two clever men hit on a plan, and proceeded to return both trucks to Austin in a matter of just a few hours.

A large grocery-store chain, Krikey's, has a promotion where their â€śKrikey Clubâ€ť customers can get discounts on automobile fuel. For every dollar a customer spends at Krikey's, they get a point. When enough points are accumulated, they can be cashed in for gas discounts at the pump. The discounts come only in 10-cent intervals: 100 points gets the shopper a 10-cent discount per gallon of gas, 200 points would fetch a 20-cent discount, and so on up to 1000 points, and the maximum discount of a dollar per gallon. Discounts can not be used for more than 35 gallons at a time.

Points that are not used by the end of each calendar month are forfeited, and each month starts a clean slate for each customer.

Shopper JesĂşs Martinez spends the equivalent of 20 dollars per day at Krikeys every month. His old car's gas tank has a 24-gallon capacity, and he uses one gallon of gas per day. Assume the price of gas for a typical month is $3.33 per gallon, and that a month is 30 days long (for ease of calculations).

The May Bonus:What is the most JesĂşs can save? And how does he do it?

Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.

The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back of the man in front, and the man in front cannot see anyone. The cannibals show the men five hats. Three of the hats are black and two of the hats are white.

Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.

The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"

The April Bonus:How did he know the color of his hat and what color was it?

Consider an irregular flat surface such as pictured below. To find the center of mass of the object, three plumb lines have been drawn, but the measurements weren't exact, and the three lines do not intersect at a single point. Instead, the three intersections lines form a triangle as shown.

The December Bonus:Assuming that the probability of finding the true center of mass on either side of each line is Â˝, what is the probability that the true center of mass is actually located within the triangle?

The November Bonus: A commuter who dabbles in mathematics has observed that, when he travels north on his
preferred interstate highway, the difference between the highway's mile markers and his own car's odometer is a
constant. (Actually, this 'constant' can change drastically for different interstate trips, and even varies a bit
during a single trip, but let's assume it's a constant for any given trip.) He has also observed that, when he's
on the same freeway southbound, the sum of the highway's mile markers and his own car's odometer is a (different)
constant.

As our commuter leaves a small town and enters the interstate, he notes that his constant for this trip is 119,163,
while if he had gone the other direction, his constant would have been 118,799.

Chapter 16 of Martin Gardnerâ€™s Wheels, Life and Other Mathematical Amusements shows how the nine non-zero
digits may be arranged in two groups so that 158x23 = 79x46, which gives the product of 3634. He tells us there are
two more solutions that arrange the same nine digits in the same pattern(three digits times two digits equals two
digits times two digits), with the two products both being larger than 3634.

The October Bonus:What are they? And can you find them without using a computer?

The July Bonus: If the game is played 900 times, with a good random number generator to pick the choices
for both players, how many fewer ties will there be with "Rock, Paper, Scissors, Lizard, Spock" than with the old
"Rock, Paper, Scissors?

Felix Unger, known for his fastidiousness and attention to detail, needs three pens for a task. Roomie Oscar
Madison's pen jar has a jumble of 30 pens â€“ eleven red, nine brown, six black, and four violet.

The June Bonus:If pens are chosen without looking, what is the minimum number of pens that Felix must
withdraw from the jar to ensure having three of the same color?

January 2013 PUZZLE - "Nyuk Nyuk - A Half a Loaf is Better than What?"

Submitted by Dave Thomas

The Three Stooges walked into a Deli to buy some bread. Moe bought half the bread remaining on the shelves, and
half of a loaf more. Larry and Curly each did the same. After they had left, the baker promptly closed the Deli,
as his bread was sold out. Surprisingly, the baker didn't need to cut even one loaf.

The January Bonus: how many loaves were on the shelves when the Stooges came in?

Couch Potato Larry doesn't like to watch commercials, so if a show he is watching goes to commercial, he'll flip to the
other network to watch actual programming. We are given this inside information: there are only two television networks,
TEE and VEE, and each runs shows for 2/3 of the time, and commercials for 1/3 of the time. So, there are three ways
things can turn out at any specific time:

Either both TEE and VEE are showing commercials;

One network is showing a commercial, while the other is showing real programming;

Both stations are showing real programming.

The December Bonus: in the long run, which scenario (1,2, or 3) is most likely? And which is least likely?

The November Bonus
In Martin Gardner's Magic Show, he describes Langford's Problem, which is to arrange four pairs of cards: two aces,
two deuces, two threes, and two fours side by side in a row so that one card separates the aces, two cards separate
the deuces and so on. What is the solution? Apparently there are no solutions with five or six pairs of cards, but
there are 26 solutions with seven pairs.

Starting with ten bowling pins in the usual position, and then removing the #2 pin, show how to remove the remaining
nine pins by jumping, checkers style, over a pin to be removed and into a vacant position. Eight pins may be removed
in six moves as follows, leaving only one pin standing:

7-2, Jumping from the #7 position over the pin on spot #4 into the vacant #2 spot, removing the pin at spot #4.

9-7, removing the pin at spot #8.

1-4, removing the pin at spot #2.

7-2, removing the pin at spot #4.

6-4, 4-1, 1-6, a triple jump removing pins at spots #5, #2, and #3.

10-3, removing the pin at spot #6.

The August Bonus
Starting with a vacancy at spot #3, show how to remove eight pins in five jumps, leaving only one pin standing.

A boat can travel at a speed of 3m/sec on still water. A boatman wants to cross a river whilst covering the shortest
possible distance.

The July BonusIn what direction should he row with respect to the bank if the speed of the water is (A) 2 m/sec, (B) 4 m/sec.? Assume that the speed of the water is the same everywhere.

Hall of Fame (July Puzzle Solvers):

Rocky S. Stone (NM)
Keith Gilbert (NM)
Eric Hanczyc (WA)

Hall of Honorable Mention (July Puzzle Partial Solvers):

Austin Moede (NM)

JUNE 2012 PUZZLE - "Paging Dr. Bayes..."

Submitted by Dave Thomas

In a large hospital, Dr. Bayes was wondering about the accuracy of a certain test for the dreaded Cambrian
Protoplasmic Ailment (CPA), which affects 1% of the general population. The test itself is touted as being 88%
accurate (this is the probability that people suffering the disease get a positive test result). Bayes finds
additional information showing that the false positive rate for the test is 8%.

The June Bonus(A) If patient John Doe gets a positive test result, what is the probability
he has CPA? (B) If patient John Doe gets a negative test result, what is the probability he has CPA?

Hall of Fame (June Puzzle Solvers):

Eric Hanczyc (WA)
Keith Gilbert (NM)
Austin Moede (NM)

MAY 2012 PUZZLE - "An N-Step Program"

Submitted by Dave Thomas

There is a long escalator of N steps in height. Young Albert likes to time how long it takes to get to the
top of the escalator when he runs different numbers of steps before riding the rest of the way.

Albert finds that, if he runs 14 steps, then it takes an additional 42 seconds to reach the top.
And, if he runs 24 steps, it only takes 27 seconds more to reach the top.

The May Bonus(A) How many steps does the escalator have? (B) How fast is the escalator moving?
(C) How long would it take to ride the whole way (no running)?
(D) What is Albert's maximum running speed with respect to the escalator?

Hall of Fame (May Puzzle Solvers):

Keith Gilbert (NM)
Eric Hanczyc (WA)
Rocky S. Stone (NM)

APRIL 2012 PUZZLE - "The Triangular Pins"

Submitted by John Geohegan

In bowling, how many of the ten pins can be placed simultaneously on their spots without forming an equilateral
triangle? Thus pins 1, 7, and 10 would form an equilateral triangle, as would pins 6,9, and 10.

Here's a problem from Martin Gardner's "Mathematical Circus" which he credited to Carl Fulves, who wrote many books
on magic: "With a 7-minute hourglass and an 11-minute hourglass, what is the quickest way to time the boiling of an
egg for 15 minutes?"

Consider these pictures, taken from a moving car with an i-phone's camera. In these images, the telephone pole,
picket fence, houses, etc. are all actually vertical, and the tilt is only an artifact of the car's motion. Note
that the skewing effect depends on distance. All the images were taken from a car moving at ~ 55 mph (to the left).
The effect is strongest for the closest objects.

Images courtesy Yvonne Ly.

The February Bonus:

If the camera is pointed at a right angle to the line of travel, and if the telephone pole
in the first image is about 12 feet away from the camera's line of travel, and if the car is moving at
about 55 mph, then the pole will appear to be tilted by about 15 degrees.
Given all that, how long does it take for this camera to save an image?

A man of height h0 = 2m is bungee jumping from a platform situated at a height h = 25m above a lake.
One end of an elastic Bungee cord is attached to his foot, and the other end is fixed to the platform.
The man drops from rest in a vertical (head-down for convenience) position.

The length and elastic properties of the bungee cord (treat it like a classical spring with constant K) are
such that the man's speed is zero at the instant his head just reaches the surface of the lake. Eventually,
the jumper ends up dangling with his head 8 meters above the water.

If the solar system were proportionally reduced so that the average distance between the Sun and the Earth were 1
meter, and the density of matter was unchanged, how far away would a 60-kg observer have to be for his or her
gravitational effect on the tiny Earth to be just equal to the tiny sun's effect?

From my father's collection: A number of identical white cubes are to have painted on each face a line through the
center of the face and parallel to one pair of edges. Thus the line on any face might be oriented in either of two
directions. How many cubes can be painted in this way so as to be distinguishable from one another? Two patterns are
distinguishable if and only if one is not a rotation of the other.

The July Bonus: How many cubes?

Hall of Fame (July Puzzle Solvers):
Rocky S. Stone (NM)

JUNE '11 PUZZLE - "Across the River Wide"

Submitted by Christopher Allan, UK.

Two boats start off to cross a river from opposite sides at the same time. They meet at a point 720 yards from the
nearest shore, reach the opposite bank, then set off in return, meeting again 400 yards from the other shore. Constant
speeds again.

A column on the march is 4 miles long. A man at the rear decides to run ahead to the front, speak briefly to
someone at the front, and run back to the rear. During this time the column has advanced 3 miles. Assume speeds
constant and instantaneous turning.

The bookworm is a staple character in puzzle literature. Ours, finding himself in a library in which the sets of
books were placed in the usual sequence, decided to sample some Shakespeare from a two-volume edition on a bottom
shelf. Beginning with the Foreword of Volume 1, and boring through in a straight line to the last page of Volume 2,
the bookworm made his way at the rate of one inch every four days. If each cover is an eight of an inch thick, and
if each volume measures three inches in thickness:

The April Bonus: How long will it take the Erudite Bookworm to digest his way through Shakespeare?

The January Bonus problem about determining the direction of bicycle travel was fascinating. Maybe our readers will find similar satisfaction in the following bicycle problems.
1. Is the ability to ride "no hands" the result of fork geometry or gyroscopic forces?
2. If you're riding "no hands" and you push forward gently on the right handlebar, which way will the bike turn?
3. If you have a friend keep a stationary riderless bicycle upright and you then reach down and push the lower pedal to the rear, which way will the bicycle move? Which way will the pedals move?
4. Since the left pedal rotates clockwise relative to the crank, why is a lefthand thread used on the pedal spindle?

Hall of Fame (March Puzzle Solvers):

Rocky Stone (NM)
Ross Goeres (NM)

TO SEE HIDDEN SOLUTION TO MARCH PUZZLE: Select text from "HERE" to

1. Is the ability to ride "no hands" the result of fork geometry or gyroscopic forces?
Ans. Fork geometry. This question was answered most persuasively by David E.H. Jones in the April 1970 issue of Physics Today, reprinted in Sept. 2006, showing the gyroscopic forces had very little effect but the fork design could result in ultra stability.

2. If you're riding "no hands" and you push forward gently on the right handlebar, which way will the bike turn?
Ans. To the right. Due to counter-steering my bike swerves very slightly to the left and then steers into a right-hand turn with no force from my left hand.

3. If you have a friend keep a stationary riderless bicycle upright and you then reach down and push the lower pedal to the rear, which way will the bicycle move?
Which way will the pedals move? Ans. The bicycle will roll backward and the pedals will rotate backwards in apparent defiance of the direction you're pushing. It's worth doing the experiment with a real bicycle.

4. Since the left pedal rotates clockwise relative to the crank, why is a left-hand thread used on the pedal spindle?
Ans. Due to the downward force on the pedal, the pedal spindle in contact with the internal threads of the crank is given a counter-clockwise torque which would loosen a right-hand. thread.

"THERE"

FEBRUARY '11 PUZZLE - "Kid Conundrum!"

Courtesy Brain Teasers Forum, BrainDen.com.

Two friends are chatting:
- Peter, how old are your children?
- Well Thomas, there are three of them and the product of their ages is 36.- That is not enough ...
- The sum of their ages is exactly the number of beers we have drunk today.- That is still not enough.
- OK, the last thing is that my oldest child wears a red hat.

C. Dennis Thron has called attention to the following passage from The Adventure of the Priory School, by
Sir Arthur Conan Doyle:

"This track, as you perceive, was made by a rider who was going from the direction of the school."
"Or towards it?"
"No, no, my dear Watson. The more deeply sunk impression is, of course, the hind wheel, upon which the weight
rests. You perceive several places where it has passed across and obliterated the more shallow mark of the front one.
It was undoubtedly heading away from the school."

The January
Bonus: (A) Does Holmes know what he's talking about?
(B) Try to determine the direction of travel for the idealized bike tracks in this diagram.

A playground race will be won by the runner who most quickly runs from a starting pole to a long North-South wall,
touching any point along the wall, and then runs to a finishing pole which is 90 feet due northeast of the starting
pole. If the wall is 70 feet west of the starting pole, what is the shortest distance the winner can run?

Just over 50 light years from Earth, the two small stars comprising Castor C orbit each other with a period of 0.8 days,
orbital speeds of 0.0004c (c=lightspeed), and a separation of about 1.39x10-7 lightyears (~1.6 million miles). Assume
that the orbital plane of Castor C contains/is parallel to the line-of-sight from Earth. If Einstein had been wrong â€“
if the light emitted by these binary stars did indeed depend on the motion of the source, and moves toward Earth at
speeds between 0.9996 and 1.0004c -- then, what would an Earth-based observer see upon training a telescope on Castor C?
(A) The two stars, both bright points moving in oscillating paths along opposite directions, with a period of just over
19 hours.
(B) Both stars, producing a continuous path of light, perhaps a very elongated ellipse.
(C) Two "necklaces" with dozens of stars in each, moving in the same direction, with stars appearing as pairs on one
side of the necklace, and disappearing as pairs on the other side.
BONUS BONUS: How large a telescope (Newton reflector diameter) would be required to actually resolve the separate
images of the binary stars?

Hall of Fame (October Puzzle Solvers):

Keith Gilbert (NM)

SEPTEMBER '10 PUZZLE - "Series-ously Infinite!"

Submitted by Dave Thomas.

Consider the replacement X ? 1 + 1/X. (A) If the first X is 1, what does the series (1, 2, 3/2, 5/3, â€¦)
converge to? (B) What do you get if you square the answer for (A), then subtract one? (C) What mathematician
am I thinking of?

Use the nine digits, 1,2,3,4,5,6,7,8,and 9, each exactly once to form two numbers which give a maximum when
multiplied together. Thus, 7128 times 56934 uses the digits properly but doesn't give the maximum possible product.

The August Bonus: What two numbers yield the maximum product?

Hall of Fame (August Puzzle Solvers):

Mike Arms(NM)
Ross Goeres (NM)
Michael Terrell (NM)

JULY '10 PUZZLE - "All Downhill From Here"

Submitted by Dave Thomas.

A physicist notes that two solid spheres of different sizes roll down a ramp at the same speeds, and similarly for two thin-walled hollow spheres, two solid cylinders, and two thin-walled hollow cylinders. When he races different shapes, however (such as a thin-walled hollow cylinder versus a solid sphere), they run at different speeds.

The July Bonus: If some solid and thin-walled hollow cylinders and spheres (four objects all together) are released simultaneously at the top of the ramp, in what order will they arrive at the bottom?

On the left, the massless scale hanging from the ceiling will read "10 kg" for the 10-kg mass shown. On the right is
a system with a similar hanging scale, supporting a massless pulley and a 10-kg mass, with one rope anchored to the
floor, as shown.

The May Puzzle: What is the reading on the Weightless Scale above the pulley?.

Two uniform rods of equal length and unequal masses are connected by a massless and frictionless
hinge. Initially, the rods are at rest, forming an equilateral triangle with a frictionless surface. At time t = 0
the lower ends of the rods begin to slide apart with only the force of gravity acting upon the system.

The March Puzzle: When the system comes to rest, how far has the hinge moved horizontally from its original position?

Simpkins and Green made arrangements to meet at the railroad station to catch the 8:00 train to Philadelphia.
Simpkins thinks that his watch is twenty-five minutes fast, although it is in fact ten minutes slow. Green thinks his watch is
twenty minutes slow, while it has actually gained five minutes.

The January Puzzle: What will happen if both men, relying upon their watches, try to arrive at the
station five minutes before train time?

A bike enthusiast often rides several miles (mostly downhill) to his favorite lunch spot, Dan's Diner. He wanted to compare his average
speed getting to the diner to his average speed for the more difficult return. The rider zeroed out his trusty Schwinn speedometer, and then used it to find
that his average speed getting to lunch was 12 miles per hour (mph). After dining, however, the rider forgot to re-set the speedometer. Upon his return from
lunch, the cyclist observed that the average cycling speed for the entire round trip was 9 mph. But, the rider still didnâ€™t know what his return
speed was.

The December Puzzle: What was the riderâ€™s average speed on his return from lunch?

An apothecary found six flasks capable of holding 16, 18, 22, 23, 24, and 34 fluid ounces respectively. He
filled some with distilled water, and then filled all but one of the rest with alcohol, noting that he had used precisely twice as much
alcohol as water.

The October Puzzle: Which flask was left over? And which flasks were used for water, and which for alcohol?

A small 3x4 chessboard has three black knights () and three white knights () as shown.

The September Puzzle: Show how to achieve the following position after 16 knight moves. (A knight moves two squares
horizontally or vertically and one square vertically or horizontally, all combined as one move):

While on an expedition to Canada, an American scientist noticed a metric conversion factor hidden in the Fibonacci Series,
which starts with two 1â€™s as the first two elements. Each subsequent element is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, â€¦ .
During numerous mental conversions between miles and kilometers, the scientist noticed that, if a given element of the series represented a distance in miles,
the following element was close to the equivalent distance in kilometers. For example, 3 miles is close to 5 kilometers; 5 miles is close to 8 kilometers,
and so on.

The August Puzzle: For which two consecutive elements of the Fibonacci series is their ratio closest to the actual number of kilometers
in a mile? For which two consecutive elements is the estimation error, in meters, the smallest?

The August UBER-Puzzle: What are the two integers less than 20 which, if taken as the first two elements of the series, yield at
least one conversion in the series with an estimation error of less than two meters?

What is "Estimation Error in Meters"? Consider 100 miles ~ 161 kilometers. The actual number of kilometers in 100.0 miles
is 100*1.609344 = 160.934 km, which is .066km (66 meters, 65.6 m for the truly geeky) from the "goal" of 161.000 km.
For 100mile ~ 161km, then, the "Estimation Error" is about 66 meters.

Adapted from "Intriguing Mathematical Problems" by Oswald Jacoby and William Benson

On the final day of his close-out sale, a merchant hastily disposed of two lamps at the bargain price of $12 apiece.
He estimated that he must have made some net profit
on the combined transactions, since he made a 25 percent profit on one, and only took a 20 percent loss on the other.

At a Seismology conference, several scientists attending Session A (Sustained Shaking Events) celebrated the meeting by having
every attendee shake hands with everyone else in the room. In the next room, all the participants of parallel Session B (Shakytown After the Big One),
similarly shook hands all around.

The June Puzzle: If the number of handshakes for Session B was exactly 50 more than for Session A, how many scientists were in Sessions A and B respectively?

There are three light switches on the ground-floor wall of a three-story house. Two of the switches do nothing, but one of
them controls a bulb on the second floor. When you begin, the bulb is off. You can only make one visit to the second floor.

The May Puzzle: How do you work out which switch is the one that controls the light?

On a desert island, five men and a monkey gather cocoanuts all day, and then sleep.
One man awakens. He divides the cocoanuts into five equal shares. There is one left over, which he gives to the monkey.
He hides his share and goes to sleep. The next man then awakens and does the same, and so on for all the men.

The April Puzzle: What is the minimum number of cocoanuts originally present?

The following problem was published as problem E163 in the American Mathematical Monthly, 1935, and reprinted by Ross Honsberger in
Mathematical Morsels, 1978, as "A Mathematical Joke" What's the answer, and what's the joke?

A man purchased at a post-office some one-cent stamps, three-fourths as many two's as one's, three-fourths as many five's as two's, and five eight-cent
stamps. He paid for them all with a single bill, and there was no change.

In the near future, many of the 50 states of the union, including New Mexico and Texas, will have different numbers of congressional representatives than at present. In the presidential electoral college, the number of electors per state equals that stateâ€™s number of congressmen, plus two (for the stateâ€™s senators). The number of congressmen is directly proportional to the stateâ€™s population.
If the future number of congressmen in Texas is eight times that of New Mexico, then New Mexico would realize 20% more clout with the electoral college than with strict proportional representation, while Texas would realize 10% less clout.

The November Bonus: What is the future number of congressional representatives nationwide? In New Mexico? In Texas?

HINT: in this hypothetical Future, the number of congressmen is NOT federally mandated as 438.

Hall of Fame (November Puzzle Solvers):John Geohegan (NM)

OCTOBER '08 PUZZLE - "MARKET MELTDOWN"

Submitted by Dave Thomas

Investor Henry â€śHankâ€ť Swank uses the services of â€śTodo Toroâ€ť discount
brokers, which charges $10.00 for each buy/sell transaction. On Monday, he used the service to buy 250
shares of FBNC (Fly By Night Corp.), at $60.00 per share. By Tuesday, these stocks had increased in
value by 60%, and Hank decided to sell. By the time the sale transaction went through, however, the
volatile stocks had lost 3/8 of their value.

Reading a social security number consisting of the 9 digits, 1 through 9 though not in that order, from left to right, the first two digits form a number divisible by 2, the first three digits form a number divisible by three, the first four digits form a number divisible by four, and so on through all nine digits so that the entire nine-digit number is divisible by 9.

As a man was strolling through downtown, he popped into the office of the Ministry of Puzzles.
He asked the receptionist "Good morning. Do you have the time?" The receptionist answered "Simply add one quarter of the
time from midnight until now to half the time from now until midnight, and you will have the correct answer."

The August Bonus: What time was it?
Double Bonus: Had the man said â€śGood afternoonâ€¦â€ť instead, what time would it have been?

A New Mexican chicken farmer hired a consultant recently laid off from Los Alamos Lab. After much study, the consultant announced that "One and a half hens can lay one and a half eggs in one and a half days."

The July Bonus: How many hens are needed for the farmer to produce a dozen eggs in six days?

A commuterâ€™s van pool drops him off behind the police station every night at 6 PM, and
his wife arrives there at exactly 6 PM to pick him up. On the first day of Daylight Savings Time,
however, the man had remembered to turn his clock an hour ahead, but his wife had forgotten
completely. Finding himself without a ride (because of his wifeâ€™s thinking that it was 5 PM),
the commuter started walking home. His wife came across him walking down the road some time later,
and picked him up for the ride back home. The commuterâ€™s wife ended up getting back home eight
minutes earlier than she had expected.

The May Bonus: How long was the
manâ€™s walk before his wife picked him
up?

The MegaGenomics Corporation placed a want ad for a position requiring knowledge of biology, mathematics and computer science. Of the 60 respondents who submitted applications, 46 had training in biology, 40 had training in mathematics, 43 had training in computer science, and 10 had no training in either biology, mathematics or computer science. There are three times as many applicants with mathematics-only backgrounds as with computer-science-only backgrounds; and, there are twice as many applicants with biology-only backgrounds as with computer-science-only backgrounds.

The April Bonus: How many of the applicants had undergone training in all three fields?

A party of three couples (Ben and Alice being one couple) enters a room and shakes hands based on these conditions:
a) Once you shake a person's hand, you do not shake with that person again.
b) Couples do not shake hands with each other.
Alice asked each person how many hands he/she shook, and everyone gave her a different answer.

A long-stemmed flower extends straight up from the bottom of a lake, extending 8 inches above the lakeâ€™s surface.
A man in a rowboat observes that, when he pulls on the flower, it touches the lakeâ€™s surface at a distance of 20
inches from the stemâ€™s original position.

On the long drive home from a field trip to fabled Shark Tooth Ridge, a paleontologist passenger observes a discrepancy between the carâ€™s digital clock and his cell phoneâ€™s digital clock. Both clocks show hours and minutes only. Sometimes the cell phone reads two minutes ahead of the carâ€™s clock, and sometimes it reads just one minute ahead.

The December Bonus:If the clocks appear to be two minutes apart for twice as long as they appear to be one minute apart, and assuming both clocks can keep perfect time, what is the actual time difference (in seconds) between the clocks?

Complete the following sentence:
In this sentence, the number of occurrences of 0 is _, of 1 is _, of 2 is _, of 3 is _, of 4 is _, of 5 is _, of 6 is _, of 7 is _, of 8 is _, and of 9 is _.
Each blank is to be filled with a numeral of one or more digits, written in decimal notation.

A large ball and a very small ball are
dropped from a height of five feet, as shown. Both balls are
perfectly elastic ("bouncy"). When the large ball bounces, it then
impacts the small ball, bouncing it upward as shown.

The October Bonus: What is the highest that the
small ball can bounce?

At what time(s) do the hour, minute, and
second hands of a 12-hour clock divide the face into three equal
segments, either precisely or as close as possible? Assume a
perfectly smooth motion, and answer to within one second.

Paranormal investigator George Bradford
had worked for months setting up an elaborate blind test of
polygraphs. And here he was at last, taking data from four
individuals who had all promised to abide by the strict experimental
protocols. The first part of the experiment had all four subjects
meet in private, where they witnessed one of their number hide a toy
bunny. Then, each subject was told to make two statements to
polygraph testers (and other observers) about the "incident": one
true, and one false. Only later, as the correct answers were
revealed, could the researchers see if the polygraph machines used
alongside were giving correct answers or not.

As the four subjects gave their two statements
each, George turned white, as he realized that simple logic would
allow the polygraph examiners to decide which statements were True or
False, making it very easy for them to cheat.

The following puzzle is from "The Surprise
Attack in Mathematical Problems", by L.A.Graham. Only the words have
been changed.

Three digits, a,b,and c have been used to form
the three digit numbers abc, bca, and cab, which have then been
multiplied to make a 9-digit product. The number 234,235,286 is not
the product, but 6 is in the proper place and the other digits are
disordered.

Derek bicycles from Abercrombie to Fitch for a
one o'clock appointment. After pedalling at a steady rate for 42
kilometers, he increases his speed by 3 km/hr and arrives at
precisely 1:00. If he hadn't increased his speed he would have been
18 minutes late, and if he had made the whole trip at the greater
speed he would have arrived, exhausted, 42 minutes early.

In the carnival game called Chuck-a-Luck, the player bets on
a number, one through six. Three dice are then rolled and if the
player's number comes up once, he receives his original bet, for
instance a dollar, plus another dollar. If his number comes up two or
three times, he receives his original bet plus another two or three
dollars. The smooth-talking game operator suggests that since the
chance of the chosen number showing up on any die is one out of six,
the player has a fifty-fifty chance of getting his number at least
once on the three dice, and the payoffs of two or three dollars make
the odds to the player's advantage.

But really, how much does the player stand to
win or lose on an average bet of one dollar?

A grassland can support 63 sheep for 5 days; or, 22 cows for
9 days; or, 16 cows and 5 sheep indefinitely. The grass grows at a
constant rate per unit time in the grassland.

Three friends Pedro, Quentin and Rhett
jointly hire the grassland for $6930. They agree that the share of
rent paid by any given friend would be determined in accordance with
the total amount of grass consumed by his pets.

You have been captured by Pirates while sailing
the Carribean, and have been brought before their gruff Captain. With
a sinister snarl, he barks "I've a chest here that holds 120 pounds
of pure gold coins. Some of these coins be decloons [10 ounces
each], and the rest be triploons [three ounces each].
Now, mate, if ye can tell me exactly how many decloons and triploons
are in my chest, ye walks away a free man. Get it wrong, and ye'll be
walkin' the Plank!" After another pirate suggested that the riddle
was perhaps overly challenging, the Captain snorted, and then offered
a hint: "Awright, matey - the number of decloons times the number of
triploons couldn't be larger!"

The August Bonus: For your
life
- how many decloons and how many triploons are in the
chest?

In a race along a two-kilometer-long track, you are
required to travel the first kilometer at an average speed of 20
km/hour.

The July Bonus: (A) How fast must you travel
on the second kilometer of track to achieve an overall average speed
of 30 km/hour? (What's your off-the-hip estimate? And your Final
Answer?) (B) How fast must you travel on the second kilometer of
track to achieve an overall average speed of 40 km/hour? (C) What
have you learned, Grasshopper, about trying to average
ratios?

(Gene Aronson has submitted the following problem in slightly
different form )

Mathematicians have shown that the following problem is
workable, even though it looks like more information might be
necessary. Knowing that it's workable makes it much easier to find
the numerical answer.

A ten-foot pole floats in a large swimming pool shaped
approximately as shown in the sketch below. As the pole makes one
circuit around the pool (BLACK boundary), both ends of
the pole bump continuously against the wall. During this circuit,
point P on the pole, six feet from one end, traces out the smaller
area labelled
A (RED boundary).

The Identification (ID) Numbers allotted to Mr. Auber and Mr.
Benatar are such that the numerical magnitude of the ID number
allotted to Mr. Benatar is greater by 10 than the numerical magnitude
of the ID number allotted to Mr. Auber. None of the two ID numbers
contained any leading zeroes.

A mutual acquaintance, Mr. Cavalli , who is aware of the above
facts ( but doesn't know the actual ID numbers of the two gentlemen),
queried Mr. Auber and Mr. Benatar in turn about the sum of the digits
in their ID Numbers. The responses elicited by him were respectively
44 and 27.

At this point, Mr. Cavalli requested Mr. Auber and Mr. Benatar
give some additional information. Both gentlemen answered with a new
question: "What are the smallest possible values for the two ID
numbers?"

Thereafter, Mr. Cavalli was able to ascertain precisely the ID
numbers of Mr. Auber and Mr. Benatar.

Weight-driven grandfather clocks use two weights. One drives
the pendulum and causes the hands to turn, the other supplies power
when the clock strikes either the hour or the half-hour. Problem #20
in L. A. Graham's "Ingenious Mathematical Problems and Methods"
reads, "A weight-driven clock, striking the hour, and a single
stroke for the half hour, is wound at 10:15 P.M. by pulling up both
weights until they are exactly even at the top. Twelve hours later,
the weights are again exactly even, but lowered 720 mm. What is the
greatest distance they separated during the interval?"

Two identical candles are lighted at the same
time. One will burn out in five hours, the other in eight hours. How
long will it be before one is 2.2 times the length of the other, if
(a) identical means the candles burn at the same
rate, and start out having different lengths, AND (b)
identical means the candles start out having the same
lengths, and burn at different rates?

A brilliant but warped scientist is persuaded to help a
Hollywood mogul make a "King Kong" sequel, not by creating a giant
ape, but by developing miniature humans, just one-hundredth their
normal height. Designers have crafted a one-hundredth-scale set for
the tiny humans to interact with a normal, life-sized gorilla.

The January Bonus (Warning - SPOILER!!) In Kong's fall from the
scaled-down Empire State building, how many times faster than normal
should the film be shot to give Kong a proper-looking plummeting
rate?

Paul lives in Española, where the price of gasoline is
$2.50 per gallon. There is a gas station near Albuquerque, 75 miles
from Paul's house, which sells gas at $2.00 per gallon; his truck
gets 30 miles per gallon. Paul schemes to save money by buying gas at
the cheaper station in Albuquerque, and then cruising around his
Española home.

The December Bonus: What is the minimum number of gallons that
Paul's gas tank(s) would have to hold in order for his scheme to be
feasible?

In 1654, Chevalier de Méré approached Blaise Pascal
with a question about a gambling game that had been played for
hundreds of years. The house would bet even money that a player would
roll at least one double-six in 24 rolls of a pair of dice.

In describing his experiences at a bargain sale, Smith says that
half his money was gone in just thirty minutes, so that he was left
with as many pennies as he had dollars before, and but half as many
dollars as before he had pennies.

New Scientist
magazine publishes a new Enigma(math puzzle) each week. In the
June 4 issue, the puzzle is to find the largest integer whose digits
are all different (and do not include 0) that is divisible by each of
its individual digits. Thus the number 248 is divisible by 2, 4, and
8 but so is 824 which is larger. The largest such integer is MUCH
less than 987,654,321. Next month the solution will show how to cut
this problem down to a reasonable size.

There was once a broker of Yeti fur, highly prized for its
luxuriant texture. This broker boasted that he took no commissions
when either buying or selling the fur. The townsfolk wondered how he
could possibly stay in business, but he was apparently quite
prosperous. After years had passed, they finally found out the
broker's secret -- he was caught using a biased scale. The rigged
scale was arranged to be an ounce per pound short when buying, and an
ounce per pound heavy when selling. The broker's final transaction
involved an amount of Yeti fur that would have given him $30.00 of
illicit profit.

The June Bonus: How much did the broker spend when buying
the fur for his last transaction?

World-renowned chemist Dr. Dweeb owned a 12-gallon jug full of
sulfuric acid, and another smaller jug. He liked to make up his
favorite 25% strength solution (with a quarter of the solution being
H2SO4, and the rest good old H2O)
with a curious procedure: first, he poured acid from the 12-gallon
jug to fill the smaller jug, and then he topped off the big jug with
water. After the acid and water had been thoroughly mixed in the big
jug, he drew off another small jugful, and again topped off the large
jug with more water, arriving at his 25% solution.

This month's puzzle might just be harder than it may at first
appear! It seems that two brothers from the famous puzzle-solving
Answer family, Bobby and Al Answer, were trying out some new hot rod
cars on the family's private race-track. Once both racers were up to
their respective speeds (Bobby's car was going 120 miles per hour,
and Al's was going 95 mph), they crossed the starting mark of the
two-mile track just as the gun went off, and then maintained their
respective speeds for 24 laps each.

The March Bonus: How much time passes until Bobby first
catches up to Al?

At what position on the two-mile track (relative to the
starting mark) does this occur?

This month's puzzle is for today's mathematically-minded college
frat rats and party-goers. The Kappa Kuppa K'rona fraternity was
planning for the Big Bash. Usually, 10 cases of Spud Beer, which is 6
and 1/4 % alcohol by volume, are required for the Bash. (There are
four 6-packs per case, and 12 ounces per beer, of course!). This
year, however, crafty funds manager George Waldo Busch calculated
that they wouldn't need to buy as many cases if they got "Beastie
Beer" instead, since that brand has a mind-numbing 15 and 5/8%
alcohol by volume.

The February Puzzle: How many cases of "Beastie Beer"
should Busch Buy for the Big Bash?